Heat up large stock pot on medium, add butter to melt and coat bottom of stock pot.
Dice onions, carrots, and celery, add to pot with butter and sauté until onions are translucent. Stir in the garlic.
Add bone broth to the pot and simmer on medium for a few minutes until the carrots are tender but not disintegrating.
Incorporate the peas -- they only need to be cooked for a few minutes.
In a separate bowl, whisk up the eggs until mixed well.
Turn up the heat on the stove until the soup has reached a medium boil.
Stir the broth mixture until it is swirling around in the pot. Very slowly, drizzle in egg mixture and continue to stir while incorporating. The eggs should cook almost immediately. You want to make sure that you are mixing as you are drizzling the egg mixture into the hot broth and not just pouring it in to avoid the eggs just clumping up in the pot.
Salt & pepper to taste. Depending on the flavor of your bone broth, you may or may not need much seasoning.